One‐Sided Coverage Intervals for a Proportion Estimated from a Stratified Simple Random Sample

Summary Using an Edgeworth expansion to speed up the asymptotics, we develop one‐sided coverage intervals for a proportion based on a stratified simple random sample. To this end, we assume the values of the population units are generated from independent random variables with a common mean within each stratum. These stratum means, in turn, may either be free to vary or are assumed to be equal. The more general assumption is equivalent to a model‐free randomization‐based framework when finite population correction is ignored. Unlike when an Edgeworth expansion is used to construct one‐sided intervals under simple random sampling, it is necessary to estimate the variance of the estimator for the population proportion when the stratum means are allowed to differ. As a result, there may be accuracy gains from replacing the normal z ‐score in the Edgeworth expansion with a t ‐score.